# Group Theory methods in Physics

Indian Institute of Technology Bombay via Swayam

Found in Physics Courses

**Provider**Swayam

**Cost**Free Online Course

**Session**Finished

**Language**English

**Certificate**Paid Certificate Available

**Duration**12 weeks long

## Overview

This group theory is pitched at beginners at UG/PG levelso that the students can appreciate the wide applications of the group theory tools in other areas of physics
INTENDED AUDIENCE : Physics background
PREREQUISITES : Linear algebra, quantum mechanics, special theory of relativity
INDUSTRY SUPPORT : This tool may be applicable at R&D department of industries

## Syllabus

**COURSE LAYOUT**

**Week 1**: Introduction to discrete groups, subgroups and generators, conjugacy classes

**Week 2**: Symmetric groups, permuation group, cycle notation

**Week 3**: Direct product groups, semi-direct product groups

**Week 4**: Symmetries of molecules, point groups and Streographic projection

**Week 5**: Matrix representation of groups, Reducible and irreducible representation

**Week 6**: Great Orthogonality Theorem and Character tables, Mulliken notation, basis

**Week 7**: Tensor product, projection operator, observables, selection rules, Molecular vibrations

**Week 8**: Continuous groups, generators, Lorentz transformations

**Week 9**: Orthogonal groups and Lie algebra

**Week 10**: Unitary groups, SU(2), SU(3), weight vector diagrams and root vector diagrams

**Week 11**: Wigner Eckart Theorem, Examples

**Week 12**: Quark model, SU(3) baryons, mesons, Wigner-Eckart theorem, hydrogen atom, dynamical symmetry